This does sound quite a bit like a variation on night terrors. My son has night terrors off and on and while getting enough sleep and reducing stress are helpful, here is the trick that really worked for us.
Figure out what time of night she typically has her first episode, and wake her up briefly about 20 to 30 minutes BEFORE that time. For my son it was typically about an hour after he fell asleep, so about 30 minutes after he fell asleep I would go and gently wake him up. Usually I did this by taking him to the bathroom and asking him to pee. (Not carrying him, got him to walk himself) I think Dr Greene's idea of the full bladder CAN be true, but I found my son peed only about half the times I took him.
Apparently. waking the child up before they get to the deep sleep phase when night terrors usually occur can short circuit the process. I found that after doing this every day for about 10 days (I forget exactly how many now) it stopped the night terrors completely. I tried stopping after the first 3 or 4 days, but they started right back up, so I kept it up. Now he has them only once in a while. If he has them 2 nights in a row, I will start the waking routine again for a few nights and they go away again.
I read about this technique on this forum:
It had a lot of other great tips too, so you might want to go post about your daughter there too.
Good luck! If you try this, let me know if it works for you.